1. Modeling with Higher-Order Differential Equations
Chapter 5
Modeling with Higher-Order
Differential Equations

3. FIGURE 5.1.1 Spring/mass system

4. FIGURE 5.1.2 Direction below the equilibrium position is positive

5. FIGURE 5.1.3 A relationship between c1 > 0, c2 > 0 and phase angle 

6. FIGURE 5.1.4 Simple harmonic motion

7. FIGURE 5.1.5 Parallel springs

8. FIGURE 5.1.6 Springs in series

9. FIGURE 5.1.7 Damping devices

10. FIGURE 5.1.8 Motion of an overdamped system

11. FIGURE 5.1.9 Motion of a critically damped system

12. FIGURE 5.1.10 Motion of an underdamped system

13. FIGURE 5.1.11 Overdamped system in Example 3

14. FIGURE 5.1.12 Critically damped system in Example 4

15. FIGURE 5.1.13 Oscillatory vertical motion of the support

16. FIGURE 5.1.14 Graph of solution in (28) of Example 6

17. FIGURE 5.1.15 Graph of solution in Example 7 for various initial velocities x1

18. FIGURE Pure resonance

19. FIGURE 5.1.17 LRC-series circuit

20. FIGURE 5.1.18 Graph for Problem 21

21. FIGURE 5.1.19 Graph for Problem 22

22. FIGURE 5.1.20 Graph for Problem 23

23. FIGURE 5.1.21 Graph for Problem 24

24. FIGURE 5.1.22 Oscillating support in Problem 39

25. FIGURE 5.1.23 Beats phenomenon in Problem 45

26. FIGURE 5.2.1 Deflection of a homogeneous beam

27. FIGURE 5.2.2 Beams with various end conditions

28. TABLE

29. FIGURE 5.2.3 Deflection curve for BVP in Example 1

30. FIGURE 5.2.4 Graphs of eigenfunctions yn = sin(nx/L), for n = 1, 2, 3, 4, 5

31. FIGURE 5.2.5 Elastic column buckling under a compressive force

32. FIGURE 5.2.6 Deflection curves corresponding to compressive forces P1, P2, P3

33. FIGURE 5.2.7 Rotating string and forces acting on it

34. FIGURE 5.2.8 Deflection of cantilever beam in Problem 7

35. FIGURE 5.2.9 Deflection of vertical column in Problem 24

36. FIGURE 5.2.10 Concentric spheres in Problem 29

37. FIGURE 5.2.11 Circular ring in Problem 30

38. FIGURE 5.2.12 Propeller shaft of the battleship USS Missouri

39. FIGURE 5.3.1 Hard and soft springs

40. FIGURE 5.3.2 Numerical solution curves

41. FIGURE 5.3.3 Simple pendulum

42. FIGURE 5.3.4 In Example 2, oscillating pendulum in (b); whirling pendulum in (c)

43. FIGURE 5.3.5 Shape of hanging telephone wires is a catenary

44. FIGURE 5.3.6 Distance to rocket is large compared to R.

45. FIGURE 5.3.7 Chain pulled upward by a constant force in Example 4

46. FIGURE 5.3.8 Graph of (21) in Example 4

47. FIGURE 5.3.9 Pursuit curve in Problem 17

48. FIGURE 5.3.10 Pursuit curve in Problem 18

49. FIGURE 5.3.11 Ballistic pendulum in Problem 19

50. FIGURE 5.3.12 Airplane drop in Problem 20

51. FIGURE 5.R.1 Rotating rod in Problem 24

52. FIGURE 5.R.2 Sliding spring/mass system in Problem 25

53. FIGURE 5.R.3 Double spring system in Problem 26

54. FIGURE 5.R.4 Spring pendulum in Problem 30

55. FIGURE 5.R.5 Pendulum in Problem 31

56. FIGURE 5.R.6 Collapse of the Tacoma Narrows Suspension Bridge